
Note that in the mean-field model this line in the \((n,T)\)  plane is identical to that in the ideal Bose gas.
At low temperatures \(T \ll m\) , one can use the non-relativistic approximation, i.e.,
\(K_2(x) \approx (\pi /(2x))^{1/2} \exp (-x)\) , at \(x\gg 1\) . It leads to the well known text-book expression for the BEC line [1]}:
\( T_{\rm BC} ~=~ \frac{2\pi }{m}~\left(\frac{n}{g\zeta (3/2)}\right)^{2/3}~,~~~~\frac{T_{\rm BC}}{m}\ll 1. \) 
